The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-operational-amplifier-state-any-7fd5

stable pending witness
2026-05-29 03:56:20 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the operational amplifier. State any key formula.
75 chars

Generation

An operational amplifier (op-amp) is a high-gain differential amplifier with very high input impedance and low output impedance, commonly used to amplify voltage signals and perform mathematical operations like addition, subtraction, integration, and differentiation. In its ideal form, it has infinite gain, infinite input impedance, and zero output impedance. The key formula for an op-amp in negative feedback configuration is: **Vout = A(V+ - V-)**, where A is the open-loop gain, V+ is the non-inverting input, and V- is the inverting input. For an ideal op-amp with negative feedback, the golden rules apply: the two input voltages are equal (V+ = V-) and no current flows into the inputs.
26 tokens in · 172 tokens out · 5387 ms · $0.0027

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5399.8 ms
Base LLM
5387.0 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0027

Trail

03:56:20 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
03:56:20 red_gate decision=pass reason=no disqualifying input patterns detected
03:56:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=172 latency_ms=5387.0 cost_usd=0.0027
03:56:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:56:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:56:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:56:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:56:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:56:26 signed hash_algo=sha256 hash=sha256:1b8720c08f5d4bf3535f626b80d6f94d07d7e787b468fd8f122d402e89b33ab2

Content hash

sha256:1b8720c08f5d4bf3535f626b80d6f94d07d7e787b468fd8f122d402e89b33ab2

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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